Risk preference based option pricing in a fractional Brownian market

We focus on a preference based approach when pricing options in a market driven by fractional Brownian motion. Within this framework we derive formulae for fractional European options using the traditional idea of conditional expectation. The obtained formulae - as well as further results - accord with classical Brownian theory and confirm economic intuition towards fractional Brownian motion. Furthermore the influence of the Hurst parameter H on the price of a European option will be analyzed. -- Fractional Brownian motion ; Conditional expectation ; Risk preference based option pricing ; Fractional option pricing ; Fractional Greeks